Peter Bunclark wrote:
>hang on I thought the numbering start Jan=1 ... Dec=10 and got interrupted
>when Julius Caesar put an extra month in and so did Augustus...

As I understand it...

The original Roman calendar (attributed to Romulus) had only ten months:
March, April, May, June, Quintilis, Sextilis, September, October,
November, December. (The first four named after deities, but the rest
merely numbered, in a fit of apathy.) The calendar stopped for winter:
those 60-some days each year were not within any calendar month.

Some decades later, the months January and February were added to cover
the winter period. From this point on traditions differ about whether
the winter months were added at the start or the end of the year, and
thus about whether the calendar year starts with January or with March.
This duality persists until the Julian reform. Month lengths were
already irregular by this time, but historians are unsure of what they
actually were.

The twelve-month year was about ten days shorter than the tropical year.
In order to keep them aligned, an intercalary month was periodically
added. When this was done February would be shortened by about five days,
and then the leap month came between February and March.

The use of the leap month was decreed by priests who would be bribed
to make years longer or shorter to manipulate the term of office of
elected officials. It was also considered unlucky to have a leap month
in a time of war, which with decade-long wars would get the calendar
well out of synch.

Julius Caesar reformed the calendar by lengthening some of the months to
get the common year up to 365 days. He replaced the use of the leap month
with a leap day, which was inserted exactly where the old leap month had
been: five days before the end of February. Hence traditionally it is
February 24, not February 29, that is the leap day. He also decreed an
arithmetic formula for use of the leap day and standardised on starting
the calendar year with January.

Quintilis was renamed after Julius Caesar. Later Sextilis was renamed
after Augustus Caesar. It is often said that the month lengths were
changed at the same time, but at least one version of that story is
fabricated and there's a distinct lack of evidence for it. Other emperors
had months renamed after themselves too, but those names didn't stick.
There's no evidence that any of them was accompanied by changes in the
lengths of months either.

I think what we can learn from this whole business is: tradition sticks;
Europeans suck at calendar design; common people will cope with ambiguous,
complicated, and silly calendars for arbitrarily long.